论文标题
关于通常双曲操作员的微钙化和Feynman繁殖器的构建
On microlocalisation and the construction of Feynman Propagators for normally hyperbolic operators
论文作者
论文摘要
本文以几何学术语为全球双曲线时空上的矢量束上的正常双曲线算子提供了全局的微钙化结构。作为一种应用，这用于概括Feynman繁殖器的Duistermaat-Hörmander构造，因此结合了最重要的非量表几何操作员。结果表明，对于通常相对于Hermitian束指标是自私的双曲线操作员，可以构建Feynman繁殖器以满足反映量子域中Hadamard State在弯曲示波器中存在的阳性特性。我们还为Dirac-Type操作员在全球双曲线时期内为Feynman繁殖器提供了更直接的构造。即使旋转器上的天然束指标并不是正定的，但在这种情况下，我们可以直接对满足阳性的Feynman繁殖物进行直接的微局部结构。
This article gives global microlocalisation constructions for normally hyperbolic operators on a vector bundle over a globally hyperbolic spacetime in geometric terms. As an application, this is used to generalise the Duistermaat-Hörmander construction of Feynman propagators, therefore incorporating the most important non-scalar geometric operators. It is shown that for normally hyperbolic operators that are selfadjoint with respect to a hermitian bundle metric, the Feynman propagators can be constructed to satisfy a positivity property that reflects the existence of Hadamard states in quantum field theory on curved spacetimes. We also give a more direct construction of the Feynman propagators for Dirac-type operators on a globally hyperbolic spacetime. Even though the natural bundle metric on spinors is not positive-definite, in this case, we can give a direct microlocal construction of a Feynman propagator that satisfies positivity.
